Have you worked with Rolled Buttercream? It's awesome stuff. Much like fondant, but tastes like buttercream you would use on cakes. I use it all the time, rather than flooding with RI and you can detail immediately instead of waiting on flooded cookie to dry

I use it all the time. It's easy, tastes great, and cuts out flooding and drying time. Just put it on, and detail over it, outline around it, whatever, I even press designs into it.

I keep a squeeze bottle with light corn syrup and those small tips that come with the squeeze bottles to use as my 'glue'

What I do is, Using a shaker of powdered sugar (like you would flour in baking cookies) I roll the RBC out VERY thin (because it is so sweet like buttercream) on a large cutting board, put my cutting board into freezer or fridge to harden a bit, put 'glue' on the cookies while that's hardening, then use my offset spatula to pick them up and place on cookie. You need to use more powdered sugar than it calls for, because it becomes greasy after it sits, and your dried RI will sometimes pop off of a greasy RBC.

AI work in royal icing. If I were doing that project, I'd do royal icing transfers. Print out a sheet of paper with as many hats as you can fit on. Lay a piece of parchment or waxed paper over top, and pipe the hats. Slide the paper out from underneath to move it to a new spot of you didn't fit 100 hats on the page.

Let them fully dry. Then flood your cookies, plop the transfer on, finish up with any borders you'd like.

Montrealconfections channel on YouTube has royal icing transfers tutorials. So does hanielas and a couple others. Doing it this way means you can work in batches and do a lot ahead of time. The transfers last indefinitely. Just keep them in a dark place so they don't fade.